2

2

6093

Binary Decision Diagrams: An Improved Variable Ordering using Graph Representation of Boolean Functions

This paper presents an improved variable ordering method to obtain the minimum number of nodes in Reduced Ordered Binary Decision Diagrams (ROBDD). The proposed method uses the graph topology to find the best variable ordering. Therefore the input Boolean function is converted to a unidirectional graph. Three levels of graph parameters are used to increase the probability of having a good variable ordering. The initial level uses the total number of nodes (NN) in all the paths, the total number of paths (NP) and the maximum number of nodes among all paths (MNNAP). The second and third levels use two extra parameters: The shortest path among two variables (SP) and the sum of shortest path from one variable to all the other variables (SSP). A permutation of the graph parameters is performed at each level for each variable order and the number of nodes is recorded. Experimental results are promising; the proposed method is found to be more effective in finding the variable ordering for the majority of benchmark circuits.

Binary decision diagrams, graph representation, Boolean functions representation, variable ordering.

1

10789

BDD Package Based on Boolean NOR Operation

Binary Decision Diagrams (BDDs) are useful data
structures for symbolic Boolean manipulations. BDDs are used in
many tasks in VLSI/CAD, such as equivalence checking, property
checking, logic synthesis, and false paths. In this paper we describe a
new approach for the realization of a BDD package. To perform
manipulations of Boolean functions, the proposed approach does not
depend on the recursive synthesis operation of the IF-Then-Else
(ITE). Instead of using the ITE operation, the basic synthesis
algorithm is done using Boolean NOR operation.

Binary Decision Diagram (BDD), ITE Operation, Boolean Function, NOR operation.